The climber's speed will be greater with the longer falls, so I would assume that would raise the force. However, the longer the amount of rope, the greater effect the dynamic properties of the rope will have.

However, for a fall on static gear the distance would make a huge amount of difference. For a fall on static gear, there is nothing to absorb the extra distance/speed. Farther fall = faster fall = harder impact.

I'm probably about to show my ignorance of all things physics, but things being equal, I would expect it not to change at all. Curious to hear an actual answer.

Ideally, it shouldn't. But, life being less than ideal...

Well, the average acceleration before the catch started would be higher for the shorter fall then for the longer fall, since the longer fall reaches higher speeds and thus air resistance becomes less negligible. Dunno how that would carry through, though.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

The climber's speed will be greater with the longer falls, so I would assume that would raise the force. However, the longer the amount of rope, the greater effect the dynamic properties of the rope will have.

However, for a fall on static gear the distance would make a huge amount of difference. For a fall on static gear, there is nothing to absorb the extra distance/speed. Farther fall = faster fall = harder impact.

Assuming for the moment that it was that simple*, what would that mean in practice?

Let's say you fall five feet with ten feet of rope out. A simple calculation would say that you would have a FF 0.5 fall. If we want to put some hard numbers on it, we could us Jay's calculator to say that the top piece would feel 9.6kN.

Now let's include that equivalent 1.5 meters for rope tightening. That means you effectively fall five feet on fifteen feet of rope, reducing the FF to .33. Our "improved" model, including knot-tightening, now says the top piece would feel 8.2kN.

So adding the knot tightening reduces the peak force by 1.4 kN, or 15%

Now what if we look at a longer fall with the same fall factor?

Let's say you fall ten feet with twenty feet of rope out. Again, FF = .5, which gives us a simple number of 9.6kN on the top piece.

Now when we include that 1.5m (or 5 feet) of knot tightening to get an "improved" FF, we get 10/25, or ff = 0.4, or 8.8kN.

So for the longer fall, the knot only reduced the peak load by 0.8kN, or 8%.

This is because as you fall farther, for a given fall factor, all the rope available to absorb the fall increases except the rope in your knot. So the farther you fall, the less the knot tightening will help. The same is true for all the other small factors (stretching runners, body deformation, etc).

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Some other practical points, with more rope out in general the rope drag increases which in turn increases the effective "fall factor" by decreasing the effective rope out in the system because of friction limiting the rope stretch on the belayer side. This in general increases the total force felt by the top piece.

Redlude - true. Your factor and mine will both are in the same direction, so it seems that longer falls will produce higher effective peak forces, for a given FF.

shockabuku wrote:

cracklover wrote:

shockabuku wrote:

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Not sure what you're getting at, then. All other factors being ignored, peak force is simply predicted by the fall factor and the rope modulus. To the best of my knowledge, to the degree that other factors are either eliminated or integrated, the measurements bear this out.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Make sense?

GO

I understand most of what you're saying. I would still like to see some data on a case where these other factors aren't involved.

I would still like to see some data on a case where these other factors aren't involved.

These data are taken from a paper by Martyn Pavier. The selected drops were performed with a 70kg steel mass and the belay was tied off. It appears that with the "other factors" removed the length of fall has no significant effect on maximum tension, at least over this limited range.

For real life falls I would wonder about the effects of belay device and belayer behavior.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Make sense?

GO

I understand most of what you're saying. I would still like to see some data on a case where these other factors aren't involved.

I am? How so? The kinetic energy, ignoring air resistance, is exactly related to distance fallen.

In reply to:

This I don't understand "the rope is always proportional to the fall distance, which is proportional to the energy."

Okay, let's take FF = 1. If we double the distance fallen, we double the amount of rope, right? With me so far? And would you agree that for every other FF that holds true? That takes care of the first two thirds of that sentence: "the rope is always proportional to the fall distance".

Then if you also agree that that the kinetic energy is equal to the fall distance times a constant.... It must be that "the rope is always proportional to the fall distance, which is proportional to the energy."

IOW, as long as you don't change gravity, the springiness of the rope, the fall factor, or the mass of the climber, the energy of the climber will always vary in exact proportion to the amount of rope available to catch the fall.

In reply to:

This statement

"So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ..."

seems only to lead to this conclusion

"the rope puts the same peak force on your gear for any given FF."

if the rope is in a linear force vs. distance relationship. I suspect that breaks down with greater fall factors, but I don't know for sure.

What do you mean "a linear force vs distance relationship"?

The question is simply this: If you ask twice the length of rope to dissipate twice the amount of energy, how can it know there is any difference? As far as the rope is concerned, it is doing exactly the same amount of work per inch.

I would still like to see some data on a case where these other factors aren't involved.

These data are taken from a paper by Martyn Pavier. The selected drops were performed with a 70kg steel mass and the belay was tied off. It appears that with the "other factors" removed the length of fall has no significant effect on maximum tension, at least over this limited range.

For real life falls I would wonder about the effects of belay device and belayer behavior.

Maybe I'm missing something, but that chart of the Pavier data doesn't seem to address the original question—what is the relationship between the fall length and the maximum impact force for a given fall factor—very well. The only fall factor where we have data for multiple fall lengths is 1.00. Here the impact force increases slightly as the fall length increases from 1 to 2 m. However, at FF = 0.90 there appear to be three drops of the same length, whose range of impact forces appears to be about the same as the range at FF = 1.00, so what could be interpreted as an increasing relationship here could be due to random error.

It seems like what we need in order to answer the original question is a dataset with multiple drops at a constant fall factor over a greater range of fall lengths.

Edit: Is the impact force in the chart for the "climber's" side of the rope? Have you compared the Pavier data to that predicted by the "standard" model? Do you know the rope modulus or impact force rating of the rope?

Hmm... in the experimental method used "the rope was tied to the trolley." So the knot *should* have an affect. Which means that longer drops should, according to what I stated earlier, give a slightly higher peak force.

However, there is this: "Table 2 provides results of the number of falls-to-failure and the maximum tension recorded in the rope..."

That "maximum tension" could be interpreted in either of two ways, either the peak force, averaged over the course of the multiple drops it took to break the rope, or the highest peak force measured over the course of drops required to break the rope.

If it's the latter, then the force listed in the chart for each data point is only the force from the one fall in which the knot was mostly tensioned after several drops, since the peak force would increase as the knot gets set tighter.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Make sense?

GO

I understand most of what you're saying. I would still like to see some data on a case where these other factors aren't involved.

I am? How so? The kinetic energy, ignoring air resistance, is exactly related to distance fallen.

Kinetic energy is the energy of motion - it starts out as zero when the fall begins and grows as the climber's speed of fall increases. The maximum kinetic energy will not be equal to the original potential energy because the climber starts to slow down as the rope begins to get tight. There is gravity pulling down and the rope pulling up at the same time while the climber is slowing to a stop. I think what you mean to say is correct, that the total energy for the rope to absorb or dissipate is the potential energy which is determined by total fall length.

In reply to:

In reply to:

This I don't understand "the rope is always proportional to the fall distance, which is proportional to the energy."

Okay, let's take FF = 1. If we double the distance fallen, we double the amount of rope, right? With me so far? And would you agree that for every other FF that holds true? That takes care of the first two thirds of that sentence: "the rope is always proportional to the fall distance".

Then if you also agree that that the kinetic energy is equal to the fall distance times a constant.... It must be that "the rope is always proportional to the fall distance, which is proportional to the energy."

IOW, as long as you don't change gravity, the springiness of the rope, the fall factor, or the mass of the climber, the energy of the climber will always vary in exact proportion to the amount of rope available to catch the fall.

I didn't understand that you meant the length of rope.

In reply to:

In reply to:

In reply to:

This statement

"So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ..."

seems only to lead to this conclusion

"the rope puts the same peak force on your gear for any given FF."

if the rope is in a linear force vs. distance relationship. I suspect that breaks down with greater fall factors, but I don't know for sure.

What do you mean "a linear force vs distance relationship"?

The springiness of the rope - I was talking about if it changes due to being overstretched. I don't know if all ropes stay in the linear regime up through factor two falls for all amounts of falling mass. If not, your argument breaks down.

The linear spring model (force=constant*change in length) for a rope only works for a certain percentage of stretch of the rope. So long as this model holds then for every additional foot of stretch there is the same additional amount of associated tension in the rope. Beyond the linear range (hard fall), for the same amount of stretch, the added tension in the rope grows non-linearly - maybe like force=constant*(change in length)^2. This means each additional foot of stretch incurs a greater additional tension than the last foot.

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Make sense?

GO

I understand most of what you're saying. I would still like to see some data on a case where these other factors aren't involved.

I am? How so? The kinetic energy, ignoring air resistance, is exactly related to distance fallen.

Kinetic energy is the energy of motion - it starts out as zero when the fall begins and grows as the climber's speed of fall increases. The maximum kinetic energy will not be equal to the original potential energy because the climber starts to slow down as the rope begins to get tight. There is gravity pulling down and the rope pulling up at the same time while the climber is slowing to a stop. I think what you mean to say is correct, that the total energy for the rope to absorb or dissipate is the potential energy which is determined by total fall length.

How is that different from what I did say? When calculating fall factor, you look at the distance the climber fell before the rope starts to catch.

In reply to:

In reply to:

In reply to:

In reply to:

This statement

"So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ..."

seems only to lead to this conclusion

"the rope puts the same peak force on your gear for any given FF."

if the rope is in a linear force vs. distance relationship. I suspect that breaks down with greater fall factors, but I don't know for sure.

What do you mean "a linear force vs distance relationship"?

The springiness of the rope - I was talking about if it changes due to being overstretched. I don't know if all ropes stay in the linear regime up through factor two falls for all amounts of falling mass. If not, your argument breaks down.

The linear spring model (force=constant*change in length) for a rope only works for a certain percentage of stretch of the rope. So long as this model holds then for every additional foot of stretch there is the same additional amount of associated tension in the rope. Beyond the linear range (hard fall), for the same amount of stretch, the added tension in the rope grows non-linearly - maybe like force=constant*(change in length)^2. This means each additional foot of stretch incurs a greater additional tension than the last foot.

I think you are confused. For a given FF, a rope will always stretch the same amount per foot of rope.

The springiness of the rope - I was talking about if it changes due to being overstretched. I don't know if all ropes stay in the linear regime up through factor two falls for all amounts of falling mass. If not, your argument breaks down.

Ignoring the other factors such as knot tightening, for a given fall factor, a given rope will always stretch the same percentage. That's because the ratio between kinetic energy and rope will be constant. And it's precisely the percent stretch in the rope that gives you the force on the gear, which is why that force is (again, ignoring those other factors) always constant (for a given rope, fall factor, and mass.)

In reply to:

The linear spring model (force=constant*change in length) for a rope only works for a certain percentage of stretch of the rope. So long as this model holds then for every additional foot of stretch there is the same additional amount of associated tension in the rope. Beyond the linear range (hard fall), for the same amount of stretch, the added tension in the rope grows non-linearly - maybe like force=constant*(change in length)^2. This means each additional foot of stretch incurs a greater additional tension than the last foot.

Maybe I'm missing something, but that chart of the Pavier data doesn't seem to address the original question—what is the relationship between the fall length and the maximum impact force for a given fall factor—very well.

You're right, it doesn't demonstrate it very well. But I was reasoning that because the data show a linear relationship between fall factor and maximum tension, regardless of fall length, they support the notion that fall length doesn't matter (in this circumstance). The fact that longer fall lengths appear for both higher and lower fall factors bolsters the argument. But it is still somewhat weak.

In reply to:

Edit: Is the impact force in the chart for the "climber's" side of the rope? Have you compared the Pavier data to that predicted by the "standard" model? Do you know the rope modulus or impact force rating of the rope?

It's the rope tension, hence the climber's side.

The model does not have a single modulus; rather there are two moduli and a damping constant. But I believe one still gets a linear FF to max tension relationship from the model so one could come up with an effective modulus for this purpose. It would be something around 25 kN.

Maybe I'm missing something, but that chart of the Pavier data doesn't seem to address the original question—what is the relationship between the fall length and the maximum impact force for a given fall factor—very well.

You're right, it doesn't demonstrate it very well. But I was reasoning that because the data show a linear relationship between fall factor and maximum tension, regardless of fall length, they support the notion that fall length doesn't matter (in this circumstance). The fact that longer fall lengths appear for both higher and lower fall factors bolsters the argument. But it is still somewhat weak.

Interestingly, there appears to be an interaction between fall length and fall factor in the data. I'll expand upon that in my next post.